Abstract:We derive the information geometry of tempered stable processes. We first compute the $\alpha$-divergence between two tempered stable processes. From the divergence, we obtain the Fisher information matrix and the $\alpha$-connection on the statistical manifold. The generalized, classical, and rapidly-decreasing tempered stable geometries are dually flat, with potential functions and canonical divergences expressed in terms of the tempering parameters. Moreover, their $\alpha$-curvature tensors vanish for every $\alpha$. The geometric results are also applied to bias reduction in maximum likelihood estimation and Bayesian predictive priors.
From: Jaehyung Choi [view email]
[v1]
Mon, 17 Feb 2025 17:07:06 UTC (16 KB)
[v2]
Thu, 1 May 2025 14:19:51 UTC (16 KB)
[v3]
Wed, 7 May 2025 11:03:16 UTC (16 KB)
[v4]
Mon, 29 Dec 2025 17:49:39 UTC (16 KB)
[v5]
Wed, 26 Aug 2026 17:11:03 UTC (30 KB)
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